| 引用本文： |
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洪玲,莫利柳,韦增欣.一个共轭梯度方法的全局收敛性[J].广西科学,2007,14(3):239-243. [点击复制]
- HONG Ling,MO Li-liu,WEI Zeng-xin.The Global Convergence of a Conjugate Gradient Method[J].Guangxi Sciences,2007,14(3):239-243. [点击复制]
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| 摘要: |
| 给出一种较弱的线搜索:寻找一个步长tk=ρjkΔk满足f(xk+ρjdk)-f(xk)≤ αρjgkTdk-m/2(ρj)2‖dk‖2,α∈(0,1),ρ∈(0,1),m>0和gk+1Tdk+1<0,将此线搜索应用于求解共轭梯度公式的βk*,得到一种新共轭梯度算法,并证明新算法具有全局收敛,用数值实验说明新算法是有效的. |
| 关键词: 无约束优化 共轭梯度法 线搜索 全局收敛性 |
| DOI： |
| 投稿时间：2006-11-29修订日期：2007-02-02 |
| 基金项目:广西自然科学基金项目(No.0542043)资助 |
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| The Global Convergence of a Conjugate Gradient Method |
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HONG Ling, MO Li-liu, WEI Zeng-xin
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| (College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| A line search is proposed.Under some suitable weak condition, we search a stepsize tk=ρjkΔk satisfying f (xk+ρjdk)-f (xk) ≤ αρjgkTdk-m/2 (ρj)2‖dk‖2, α∈ (0, 1), ρ∈ (0, 1), m>0 and gk+1Tdk+1<0.A new algorithm is obtained by using the present line search, and its global convergence is proved.Preliminary numerical results show that this method is efficient. |
| Key words: unconstrained optimization conjugate gradient method line search global convergence |
